The next generation mobile wireless communication system (5G) or new radio (NR), will support a diverse set of use cases and a diverse set of deployment scenarios. The latter includes deployment at both low frequencies (100s of MHz), similar to LTE today, and very high frequencies (mm waves in the tens of GHz).
Similar to Long Term Evolution (LTE), NR uses Orthogonal Frequency Division Multiplexing (OFDM) in the downlink (i.e., from a network node such as a gNodeB (gNB), eNB, or base station, to a wireless device such as a user equipment or UE) and uplink (i.e. from wireless device to network node). In the uplink both discrete Fourier transform (DFT)-spread OFDM (DFT-S-OFDM) and OFDM are supported.
The basic NR physical resource can thus be seen as a time-frequency grid similar to the one in LTE as illustrated in FIG. 1, where each resource element corresponds to one OFDM subcarrier during one OFDM symbol interval. FIG. 1 is a diagram of LTE physical resources. Although a subcarrier spacing of Δf=15 kHz is shown in FIG. 1, different subcarrier spacing values are supported in NR. The supported subcarrier spacing values (also referred to as different numerologies) in NR are given by Δf=(15×2α) kHz where α is a non-negative integer.
Furthermore, the resource allocation in LTE is typically described in terms of resource blocks (RBs), where a resource block corresponds to one slot (0.5 ms) in the time domain and 12 contiguous subcarriers in the frequency domain. Resource blocks are numbered in the frequency domain, starting with 0 from one end of the system bandwidth. For NR, a resource block is also 12 subcarriers in frequency. A RB is also referred to as physical RB (PRB) in the rest of sections.
In the time domain, downlink and uplink transmissions in NR will be organized into equally-sized subframes similar to LTE as shown in FIG. 2. FIG. 2 is a diagram of an LTE time-domain structure with 15 kHz subcarrier spacing. In NR, the subframe length is also 1 ms regardless of numerology configured. A subframe is further divided into slots. For 15 kHz subcarrier spacing, there is one 14-symbol slot, or two 7-symbol slots per subframe. For subcarrier spacing of greater than 15 kHz, there are more slots per subframe.
Downlink transmissions in LTE and NR are dynamically scheduled, i.e., in each subframe or slot, the network node transmits downlink control information (DCI) about which wireless device data is to be transmitted to and which resource blocks in the current downlink subframe the data is transmitted on. This control signaling is typically transmitted in the first few OFDM symbols in each subframe in LTE and each slot in NR. The control information is carried on the Physical Downlink Control Channel (PDCCH) and data is carried on the Physical Downlink Shared Channel (PDSCH). A wireless device first detects and decodes the PDCCH and if a PDCCH is decoded successfully, it then decodes the corresponding PDSCH based on the decoded control information in the PDCCH. Each wireless device is assigned with a C-RNTI (Cell Radio Network Temporary Identifier), which is unique within the serving cell. The C-RNTI is used to scramble the CRC (cyclic redundancy check) bits of the PDCCH intended for the wireless device. A wireless device recognizes its PDCCH by checking the C-RNTI used to scramble the CRC (cyclic redundancy check) bits of the PDCCH.
Uplink data transmission are also dynamically scheduled using the PDCCH. Similar to downlink, a wireless device first decodes uplink grants in the PDCCH and then transmits data over the Physical Uplink Shared Channel (PUSCH) based on the decoded control information in the uplink grant such as modulation order, coding rate, uplink resource allocation, etc.
In LTE, semi-persistent scheduling (SPS) is also supported in both uplink and downlink, in which periodic data transmissions are activated or deactivated by the PDCCH. After the first SPS activation, there is no PDCCH transmitted for the subsequent data transmissions. The CRC bits of the PDCCH used for SPS activation or deactivation are scrambled by SPS-C-RNTI, which is configured for a wireless device if the wireless device supports SPS.
In addition to the PUSCH, the Physical Uplink Control Channel (PUCCH) is also supported in NR to carry uplink control information (UCI) such as HARQ (Hybrid Automatic Repeat Request) related Acknowledgement (ACK), Negative Acknowledgement (NACK), or Channel State Information (CSI) feedback.
Although many details of NR PUCCH are still to be determined, it is envisioned that, similar to LTE, PUCCH resources will be pre-allocated in a cell and shared by all wireless devices.
PUCCH in LTE
LTE uses hybrid-ARQ, where, after receiving downlink data in a subframe, the terminal attempts to decode it and reports to the base station whether the decoding was successful (ACK) or not (NAK). In case of an unsuccessful decoding attempt, the network node can retransmit the erroneous data.
Uplink control information (UCI) transmitted from the wireless device to the network node consists of:                HARQ-ACK/NACK for received downlink data;        Downlink CSI; and        Scheduling requests (SRs), indicating that a mobile terminal needs uplink resources for uplink data transmissions.This UCI information is carried on the Physical Uplink Control Channel (PUCCH). In order to provide frequency diversity, frequency resources for the PUCCH are switched on the slot boundary, i.e., one RB consists of 12 subcarriers at the upper part of the spectrum in the first slot of a subframe and another RB at the lower part of the spectrum during the second slot of the subframe or vice versa. This is often referred to as PUCCH frequency hopping. An example is shown in FIG. 3. FIG. 3 is a diagram of an Uplink L1/L2 control signaling transmission on the PUCCH. If more resources are needed for the uplink control signaling, e.g., in case of very large overall transmission bandwidth supporting a large number of users, additional resources blocks can be assigned next to the previously assigned resource blocks.PUCCH Formats        
There are 5 PUCCH formats defined in LTE, i.e., PUCCH format 1 to format 5, each capable of carrying a different number of UCI bits. The following is a list of combinations of UCI on different PUCCH formats in LTE:                Format 1 for positive scheduling requests (SR).        Format 1a for 1-bit HARQ-ACK or for 1-bit HARQ-ACK with positive SR.        Format 1b for 2-bit HARQ-ACK or for 2-bit HARQ-ACK with positive SR.        Format 2 for a CSI report when not multiplexed with HARQ-ACK.        Format 2a for a CSI report multiplexed with 1-bit HARQ-ACK for normal cyclic prefix.        Format 2b for a CSI report multiplexed with 2-bit HARQ-ACK for normal cyclic prefix.        Format 2 for a CSI report multiplexed with HARQ-ACK for extended cyclic prefix.        Format 3 for up to 10-bit HARQ-ACK for FDD and for up to 20-bit HARQ-ACK for TDD.        Format 3 for up to 11-bit corresponding to 10-bit HARQ-ACK and 1-bit positive/negative SR for FDD and for up to 21-bit corresponding to 20-bit HARQ-ACK and 1-bit positive/negative SR for TDD.        Format 3 for HARQ-ACK, 1-bit positive/negative SR (if any) and CSI report(s).        Format 4 for more than 22 bits of UCI including HARQ-ACK, SR (if any) and periodic CSI report(s) (if any).        Format 5 for more than 22 bits of UCI including HARQ-ACK, SR (if any) and periodic CSI report(s) (if any).        Format 4 for more than one CSI report and SR (if any).        Format 5 for more than one CSI report and SR (if any).        
PUCCH format 1 is used for carrying SR only, while PUCCH format 1a/1b are used to carry one or two bits ACK/NACK information, respectively, or one or two bits ACK/NACK with SR.
A CSI report consists of multiple bits per subframe. Transmission of CSI reports on the PUCCH is handled by PUCCH formats 2, 3, 4, and 5, which are capable of multiple information bits per subframe.
PUCCH format 2 can carry a payload of at most 11 bits. Variants of format 2 are format 2a and 2b which also carries HARQ-ACK information of 1 and 2 bits, respectively, for normal cyclic prefix. For extended cyclic prefix, PUCCH Format 2 can also carry HARQ-ACK information. For simplicity, they are all referred to as format 2 herein.
PUCCH format 3 is designed to support larger HARQ-ACK payloads to support carrier aggregation (CA) with up to 5 component carriers (CCs), and can carry up to 10 or 20 HARQ-ACK bits for FDD and TDD, respectively. PUCCH format 3 can also carry SR, and support up to 21 bits total. PUCCH format 3 can also carry CSI.
Information bits or symbols for PUCCH formats 1-3 are code division multiplexed on to a RB. Different wireless devices can be semi-statically configured with particular PUCCH formats 1-3 resources and multiple wireless devices can be supported in the same RB.
PUCCH formats 4 and 5 carry still larger payloads, mainly used for carrier aggregation (CA) with up to 32 component carriers (CCs). PUCCH format 4 can be configured with up to 8 RBs. PUCCH format 5 occupies one RB and UCI for two WDs can be multiplexed in the same RB.
PUCCH uses either BPSK or QPSK modulation. Table 1 is a summary of the supported PUCCH formats in LTE.
TABLE 1Supported PUCCH formats in LTENumber ofPUCCHModulationcoded bitsNumber of UCI bits performatschemeper subframesubframe1N/AN/AN/A1aBPSK111bQPSK222QPSK20Up to 112aQPSK + BPSK21Up to 112bQPSK + QPSK22Up to 113QPSK48Up to 10 for FDD and 20for TDD4QPSKUp to 288 per PRB>225QPSKUp to 144 per PRB>22Transmission SchemesIn LTE, multiple transmission schemes are supported including:                Single antenna port scheme;        Transmit diversity scheme;        Large delay CDD (Cyclic Delay Diversity) scheme;        Close-loop spatial multiplexing scheme;        Multi-user MIMO (Multiple Input and Multiple Output) scheme;        Dual layer scheme; and        Up to 8 layer transmission scheme.        
In addition, there are ten transmission modes (TMs), i.e., Mode 1 to Mode 10. Each Transmission mode is associated with a transmission scheme. A wireless device is semi-statically configured with one transmission mode. For each transmission mode, the CSI contents are generally different. For example, TM3 is associated with a large delay CDD scheme, generally referred to as open-loop transmission mode. In TM3, a precoder matrix indication (PMI) is not reported in CSI and only one channel quality indication (CQI) is reported regardless of rank 1 or rank 2. TM4 is associated with a closed-loop spatial multiplexing scheme, generally referred to as closed-loop transmission mode. The CSI report includes PMI, rank indication (RI) and CQI. TM9 is associated with the “up to 8 layer transmission scheme” and the CSI report in this TM includes RI, PMI and CQI. However, in LTE Third Generation Partnership Project (3GPP) Release-14 (referred to as Rel-14), semi-open-loop transmission and an advanced CSI codebook were introduced to TMs 9 and 10 and the CSI contents are different in each case. For semi-open-loop, either no PMI or partial PMI is fed back depending on the number of antennas and codebooks used. For advanced codebook based CSI, higher resolution CSI is fed back from wireless device to base station and there are more CSI bits to feedback. TM10 is also associated with the “up to 8 layer transmission scheme” but can support CSI feedback for more than one serving transmission point or cell, so it is often referred as the CoMP (Coordinated Multiple Transmission Point) mode. In general, the CSI contents and payload size are different for different TMs.
LTE supports carrier aggregation of up to 32 component carriers (CCs) in the downlink. Each CC acts as a cell and one of them is a primary cell or carrier. Only the primary carrier may have an associated uplink carrier. In this case, ACK/NACK, SR, and CSI for each downlink component carrier are aggregated and transmitted on the single uplink carrier. The aggregated UCI payload size thus can be quite large.
To simplify the transmission schemes, NR will support only two transmission schemes, i.e.:
Scheme 1: Closed loop transmission
Scheme 2: Open loop and semi-open loop transmission
Dynamic switching between transmission schemes may be supported. Carrier aggregation may also be supported in NR.
CSI-RS Transmission
Similar to LTE, in NR a unique reference signal is transmitted from each antenna port at the network node for downlink channel estimation at a wireless device. Reference signals for downlink channel state estimation measurements are commonly referred to as channel state information reference signal (CSI-RS). For N antenna ports, N CSI-RS signals are required, each associated with one antenna port.
By measuring on CSI-RS, a wireless device can estimate the effective channel the CSI-RS is traversing including the radio propagation channel and antenna gains at both the network node and the wireless device. Mathematically, this implies that if a known CSI-RS signal xi (i=1, 2, . . . , Ntx) is transmitted on the ith transmit antenna port at network node, the received signal yj (j=1, 2, . . . , Nrx) on the jth receive antenna port of a wireless device can be expressed asyj=hi,jxi+nj where hi,j is the effective channel between the ith transmit antenna port and the jth receive antenna port, nj is the receiver noise associated with the jth receive antenna port, Ntx is the number of transmit antenna ports at the network node and Nrx is the number of receive antenna ports at the wireless device.
A wireless device can estimate the Nrx×Ntx effective channel matrix H (H(i,j)=hi,j) and thus the channel rank, precoding matrix, and channel quality. This is achieved by using a predesigned codebook for each rank, with each codeword in the codebook being a precoding matrix candidate. A wireless device searches through the codebook to find a rank, a codeword associated with the rank, and channel quality associated with the rank and precoding matrix to best match the effective channel and the noise. The rank, the precoding matrix and the channel quality are reported in the form of a rank indicator (RI), a precoding matrix indicator (PMI) and a channel quality indicator (CQI) as part of CSI feedback. This results in so-called channel dependent precoding, or closed-loop precoding. Such precoding essentially strives to focus the transmit energy into a subspace which is strong in the sense of conveying much of the transmitted energy to the wireless device.
A CSI-RS signal is transmitted on a set of time-frequency resource elements (REs) associated with an antenna port. For channel estimation over the whole system bandwidth, CSI-RS is typically transmitted over the whole system bandwidth. The set of REs used for CSI-RS transmission in a subframe is referred to as a CSI-RS resource. From a wireless device perspective, an antenna port is equivalent to a CSI-RS that the wireless device shall use to measure the channel. Up to 32 (i.e. Ntx=32) antenna ports are supported in NR and thus 32 CSI-RS signals can be configured for a wireless device.
In NR, the following three types of CSI-RS transmissions are supported:                Periodic CSI-RS Transmission: CSI-RS is transmitted periodically in certain subframes. This CSI-RS transmission is semi-statically configured using parameters such as CSI-RS resource, periodicity and subframe offset similar to LTE.        Aperiodic CSI-RS Transmission: This is a “one-shot” CSI-RS transmission that can happen in any subframe. One-shot signifies that CSI-RS transmission only happens once per trigger. The CSI-RS resources (i.e., the resource element locations which consist of subcarrier locations and OFDM symbol locations) for aperiodic CSI-RS are semi-statically configured. The transmission of aperiodic CSI-RS is triggered by dynamic signaling through the PDCCH. The triggering may also include selecting a CSI-RS resource from multiple CSI-RS resources.        Semi-Persistent CSI-RS Transmission: Similar to periodic CSI-RS, resources for semi-persistent CSI-RS transmissions are semi-statically configured with parameters such as periodicity and subframe offset. However, unlike periodic CSI-RS, dynamic signaling is needed to activate and possibly deactivate the CSI-RS transmissions. An example is shown in FIG. 4. In particular, FIG. 4 shows the timing of semi-persistent CSI-RS transmission.In NR, two types of CSI feedback may be supported for closed-loop transmission, i.e., Type I and Type II.        
Type I is codebook based PMI feedback with normal resolution targeting single-user MIMO (SU-MIMO) transmissions
Type II is an enhanced CSI feedback with higher resolution targeting multi-user MIMO (MU-MIMO) transmissions
Two different codebooks will be designed for the two feedback types. With Type II feedback, there are more bits for PMI feedback than in Type I.
CSI Reporting:
In LTE, wireless devices can be configured to report CSI in periodic or aperiodic reporting modes. Periodic CSI reporting is carried on the PUCCH while aperiodic CSI is carried on the PUSCH. The PUCCH is transmitted on one or more preconfigured numbers of physical resource blocks (PRBs) and uses a single spatial layer with quadrature phase shift keying (QPSK) modulation. PUSCH resources carrying aperiodic CSI reporting are dynamically allocated through uplink grants carried over the PDCCH or the enhanced PDCCH (EPDCCH), and can occupy a variable number of PRBs, use modulation states such as QPSK, 16 quadrature amplitude modulation (QAM), and 64 QAM, as well as multiple spatial layers. So the PUSCH is more flexible in terms of resource allocation in adapting to UCI payload size and also modulation/coding rate in adapting to the channel conditions.
In LTE, a periodic CSI report can occur in the same subframes as those containing SPS PUSCH, in which case the periodic CSI reports are piggy backed on the PUSCH. This allows periodic CSI to be transmitted using link adaptation, and so periodic CSI can be transmitted in a more spectrally efficient manner than on the PUCCH (which always uses QPSK with a fixed number of resources). However, periodic CSI reports are formed such that they fit in the preconfigured small payload of the PUCCH, and so may carry less information even when they are piggy backed on the PUSCH, for example by the use of codebook subsampling. By contrast, aperiodic CSI reporting on the PUSCH uses the full resolution of the CSI feedback, and is not subsampled. Furthermore, periodic CSI reporting in LTE requires that at least one PUCCH resource be configured for the wireless device, which is a waste of PUCCH resources which are reserved and may be unused even if the periodic CSI is always carried on PUSCH. Therefore, while LTE can transmit periodic CSI on PUSCH with semi-persistent resource allocation, such CSI is generally less accurate than aperiodic CSI on PUSCH
In LTE, the PDCCH uplink (UL) grant allocates a single resource for all content to be carried on the PUSCH, including UL-SCH (UL Shared Channel, carried on PUSCH), CSI (including RI, CRI (CSI-RS resource indicator), relative power indicator (RPI), CQI, and PMI), and HARQ-ACK. (Because the size of the message is determined according to the reported RI, CRI, and/or RPI when CSI is piggy backed on the PUSCH, the network node does not know at the time of the UL grant what the size of the UL CSI will be. The network node must therefore allocate extra resources to ensure that both the CSI and the other content will fit on the PUSCH resource. It should also be noted that CSI on the PUSCH always carries complete CSI messages for each cell, CSI process, and/or eMIMO-Type: all configured parameters (i.e., one or more of RI, CRI, RPI, CQI, PMI) to be reported for the cell, CSI process, and/or eMIMO-type are reported together in one transmission on the PUSCH.
The wireless device is generally required to update each new CSI report whether it is reported periodically or aperiodically. However, if the number of CSI reports to be produced is greater than the number of CSI processes, the wireless device is not required to update the CSI report in order to limit the wireless device computation complexity. This does not however signify that the wireless device is forbidden from updating the report, and so whether a CSI report will be identical to a prior transmitted report in this case is not known.
In NR, in addition to periodic and aperiodic CSI reporting as in LTE, semi-persistent CSI reporting will also be supported. Thus, three types of CSI reporting will be supported in NR as follows:                Periodic CSI Reporting: CSI is reported periodically by the wireless device. Parameters such as periodicity and subframe offset are configured semi-statically using higher layer signaling from the network node to the wireless device.        Aperiodic CSI Reporting: This type of CSI reporting involves a single-shot (i.e., one time) CSI report by the wireless device which is dynamically triggered by the network node, e.g. by the DCI in the PDCCH. Some of the parameters related to the configuration of the aperiodic CSI report is semi-statically configured from the network node to the wireless device but the triggering is dynamic.        Semi-Persistent CSI Reporting: similar to periodic CSI reporting, semi-persistent CSI reporting has a periodicity and subframe offset which may be semi-statically configured by the network node to the wireless device. However, a dynamic trigger from the network node to wireless device may be needed to allow the wireless device to begin semi-persistent CSI reporting. In some cases, a dynamic trigger from network node to wireless device may be needed to command the wireless device to stop the semi-persistent transmission of CSI reports.With regard to CSI-RS transmission and CSI reporting, the following combinations will be supported in NR:        For periodic CSI-RS transmission                    Semi-persistent CSI reporting is dynamically activated/deactivated;            Aperiodic CSI reporting is triggered by DCI.                        For semi-persistent transmission of CSI-RS,                    Semi-persistent CSI reporting is activated/deactivated dynamically;            Aperiodic CSI reporting is triggered by DCI.                        For aperiodic transmission of CSI-RS,                    Aperiodic CSI reporting is triggered by DCI;            Aperiodic CSI-RS is triggered dynamically.CSI Frame Work in NR:                        
In NR, a wireless device can be configured with N≥1 CSI reporting settings, M≥1 Resource settings, and one CSI measurement setting, where the CSI measurement setting includes L≥1 links and the value of L may depend on the wireless device capability. At least the following configuration parameters are signaled via RRC at least for CSI acquisition.                N, M, and L are indicated either implicitly or explicitly.        In each CSI reporting setting, at least: reported CSI parameter(s), CSI Type (I or II) if reported, codebook configuration including codebook subset restriction, time-domain behavior, frequency granularity for CQI and PMI, measurement restriction configurations.        In each Resource setting:                    A configuration of S≥1 CSI-RS resource set(s);            A configuration of Ks≥1 CSI-RS resources for each set s, including at least: mapping to REs, the number of ports, time-domain behavior, etc.;            Time domain behavior: aperiodic, periodic or semi-persistent;            RS type which encompasses at least CSI-RS.                        In each of the L links in CSI measurement setting: CSI reporting setting indication, Resource setting indication, quantity to be measured (either channel or interference)                    One CSI reporting setting can be linked with one or multiple Resource settings;            Multiple CSI reporting settings can be linked.At least, the following are dynamically selected by L1 or L2 signaling, if applicable.                        One or multiple CSI reporting settings within the CSI measurement setting;        One or multiple CSI-RS resource sets selected from at least one Resource setting;        One or multiple CSI-RS resources selected from at least one CSI-RS resource set.Control Signaling        
LTE control signaling can be carried in a variety of ways, including carrying control information on the PDCCH or the PUCCH, embedded in the PUSCH, in medium access control (MAC) control elements (“MAC CEs”), or in radio resource control (RRC) signaling. Each of these mechanisms is customized to carry a particular kind of control information.
Control information carried on the PDCCH, the PUCCH, or embedded in (‘piggy backed on’) the PUSCH is physical layer related control information, such as downlink control information (DCI), uplink control information (UCI), as described in 3GPP Technical Specification (TS) 36.211, 36.212, and 36.213. DCI is generally used to instruct the wireless device to perform some physical layer function, providing the needed information to perform the function. UCI generally provides the network with needed information, such as HARQ-ACK, scheduling request (SR), channel state information (CSI), including CQI, PMI, RI, and/or CRI. UCI and DCI can be transmitted on a subframe-by-subframe basis, and so are designed to support rapidly varying parameters, including those that can vary with a fast fading radio channel. Because UCI and DCI can be transmitted in every subframe, UCI or DCI corresponding to a given cell tend to be on the order of tens of bits, in order to limit the amount of control overhead.
Control information carried in MAC CEs is carried in MAC headers on the uplink and downlink shared transport channels (UL-SCH and DL-SCH), as described in 3GPP TS 36.321. Since a MAC header does not have a fixed size, control information in MAC CEs can be sent when it is needed, and does not necessarily represent a fixed overhead. Furthermore, MAC CEs can carry larger control payloads efficiently, since they are carried in UL-SCH or DL-SCH transport channels, which benefit from link adaptation, HARQ, and can be turbo coded. MAC CEs are used to perform repetitive tasks that use a fixed set of parameters, such as maintaining timing advance or buffer status reporting, but these tasks generally do not require transmission of a MAC CE on a subframe-by-subframe basis. Consequently, channel state information related to a fast fading radio channel, such as PMI, CQI, RI, and CRI are not carried in MAC CEs in LTE up to Rel-14.
2D Antenna Arrays
Such antenna arrays may be (partly) described by the number of antenna columns corresponding to the horizontal dimension Nh, the number of antenna rows corresponding to the vertical dimension Nv and the number of dimensions corresponding to different polarizations Np. The total number of antennas is thus N=NhNvNp. It should be pointed out that the concept of an antenna is non-limiting in the sense that it can refer to any virtualization (e.g., linear mapping) of the physical antenna elements. For example, pairs of physical sub-elements could be fed the same signal, and hence share the same virtualized antenna port. An example of a 4×4 array with cross-polarized antenna elements is illustrated in FIG. 5. In particular, FIG. 5 is a block diagram of a two-dimensional (m×1) antenna array of cross-polarized antenna elements (Np=2), with Nh=4 horizontal antenna elements and Nv=4 vertical antenna elements.
Precoding may be interpreted as multiplying the signal with different beamforming weights for each antenna prior to transmission. A typical approach is to tailor the precoder to the antenna form factor, i.e., taking into account Nh,Nv and Np when designing the precoder codebook. Such 2D codebooks may not strictly relate vertical or horizontal dimensions to the dimensions that antenna ports are associated with. Therefore, 2D codebooks can be considered to have a first and a second number of antenna ports N1 and N2, wherein N1 can correspond to either the horizontal or vertical dimension, and so N2 corresponds to the remaining dimension. That is, if N1=Nh, then N2=Nv, while if N1=Nv, then N2=Nh. Similarly, 2D codebooks may not strictly related antenna ports to polarization, and be designed with cophasing mechanisms used to two combine beams or two antenna ports, as described in the following section.
DFT-Based Precoders
A common type of precoding is to use a DFT-precoder, where the precoder vector used to precode a single-layer transmission using a single-polarized uniform linear array (ULA) with N1 antennas is defined as
                                          w                          1              ⁢              D                                ⁡                      (                          l              ,                              N                1                            ,                              O                1                                      )                          =                              1                                          N                1                                              ⁡                      [                                                                                e                                          j                      ⁢                                                                                          ⁢                      2                      ⁢                                              π                        ·                        0                        ·                                                  l                                                                                    O                              1                                                        ⁢                                                          N                              1                                                                                                                                                                                                                                            e                                          j                      ⁢                                                                                          ⁢                      2                      ⁢                                              π                        ·                        1                        ·                                                  l                                                                                    O                              1                                                        ⁢                                                          N                              1                                                                                                                                                                                                                        ⋮                                                                                                  e                                          j                      ⁢                                                                                          ⁢                      2                      ⁢                                              π                        ·                                                  (                                                                                    N                              1                                                        -                            1                                                    )                                                ·                                                  l                                                                                    O                              1                                                        ⁢                                                          N                              1                                                                                                                                                                                                ]                                              Equation        ⁢                                  ⁢        1            where l=0, 1, . . . O1N1−1 is the precoder index and O1 is an integer oversampling factor. A precoder for a dual-polarized uniform linear array (ULA) with N1 antennas per polarization (and so 2N1 antennas in total) can be similarly defined as
                                          w                                          1                ⁢                D                            ,              DP                                ⁡                      (                          l              ,                                                N                                      1                    ,                                                  ⁢                                  O                  1                                                      )                          =                              [                                                                                                      w                                              1                        ⁢                        D                                                              ⁡                                          (                      l                      )                                                                                                                                                              e                                              j                        ⁢                                                                                                  ⁢                        ϕ                                                              ⁢                                                                  w                                                  1                          ⁢                          D                                                                    ⁡                                              (                        l                        )                                                                                                                  ]                    =                                    [                                                                                                                  w                                                  1                          ⁢                          D                                                                    ⁡                                              (                        l                        )                                                                                                  0                                                                                        0                                                                                                      w                                                  1                          ⁢                          D                                                                    ⁡                                              (                        l                        )                                                                                                        ]                        ⁡                          [                                                                    1                                                                                                              e                                              j                        ⁢                                                                                                  ⁢                        ϕ                                                                                                        ]                                                          Equation        ⁢                                  ⁢        2            where ejϕ is a cophasing factor between the two polarizations that may for instance be selected from a QPSK alphabet ϕ∈
      {          0      ,              π        2            ,      π      ,                        3          ⁢          π                2              }    .
A corresponding precoder vector for a two-dimensional uniform planar arrays (UPA) with N1×N2 antennas can be created by taking the Kronecker product of two precoder vectors as w2D(l,m)=w1D(l,N1,O1)⊗w1D(m,N2,O2), where O2 is an integer oversampling factor in the N2 dimension. Each precoder w2D(l,m) forms a DFT beam, all the precoders {w2D(l,m), l=0, . . . , N1O1−1; m=0, . . . , N2O2−1} form a grid of DFT beams. An example is shown in FIG. 6, where (N1,N2)=(4,2) and (O1,O2)=(4,4). In particular, FIG. 6 is a diagram of an example of oversampled DFT beams with (N1,N2)=(4,2) and (O1,O2)=(4,4). Throughout the following sections, the terms ‘DFT beams’ and ‘DFT precoders’ are used interchangeably.
More generally, a beam with an index pair (l,m) can be identified by the direction in which the greatest energy is transmitted when precoding weights w2D(l,m) are used in the transmission. Also, a magnitude taper can be used with DFT beams to lower the beam's sidelobes. A 1D DFT precoder along N1 and N2 dimensions with magnitude tapering can be expressed as
                    w                  1          ⁢          D                    ⁡              (                  l          ,                      N            1                    ,                      O            1                    ,          β                )              =                  1                              N            1                              ⁡              [                                                                              β                  0                                ⁢                                  e                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                          π                      ·                      0                      ·                                              l                                                                              O                            1                                                    ⁢                                                      N                            1                                                                                                                                                                                                                                        β                  1                                ⁢                                  e                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                          π                      ·                      1                      ·                                              l                                                                              O                            1                                                    ⁢                                                      N                            1                                                                                                                                                                                                      ⋮                                                                                            β                                                            N                      1                                        -                    1                                                  ⁢                                  e                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                          π                      ·                                              (                                                                              N                            1                                                    -                          1                                                )                                            ·                                              l                                                                              O                            1                                                    ⁢                                                      N                            1                                                                                                                                                                                  ]              ,          ⁢                    w                  1          ⁢          D                    ⁡              (                  m          ,                      N            2                    ,                      O            2                    ,          γ                )              =                  1                              N            2                              ⁡              [                                                                              γ                  0                                ⁢                                  e                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                          π                      ·                      0                      ·                                              m                                                                              O                            2                                                    ⁢                                                      N                            2                                                                                                                                                                                                                                        γ                  1                                ⁢                                  e                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                          π                      ·                      1                      ·                                              m                                                                              O                            2                                                    ⁢                                                      N                            2                                                                                                                                                                                                      ⋮                                                                                            γ                                                            N                      2                                        -                    1                                                  ⁢                                  e                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                                          π                      ·                                              (                                                                              N                            2                                                    -                          1                                                )                                            ·                                              m                                                                              O                            2                                                    ⁢                                                      N                            2                                                                                                                                                                                  ]              ,where 0<βi, γk≤1 (i=0, 1, . . . , N1−1; k=0, 1, . . . , N2−1) are amplitude scaling factors. βi=1, γk=1 (i=0, 1, . . . , N1−1; k=0, 1, . . . , N2−1) correspond to no tapering. DFT beams (with or without a magnitude taper) have a linear phase shift between elements along each of the two dimensions. Without loss of generality, we assume that the elements of w(l,m) are ordered according to w(l,m)=w1D(l,N1,O1,β)⊗w1D(m,N2,O2,γ) such that adjacent elements correspond to adjacent antenna elements along dimension N2, and elements of w(l,m) spaced N2 apart correspond to adjacent antenna elements along dimension N1. Then the phase shift between two elements ws1(l,m) and ws2(l,m) of w(l,m) can be expressed as:
            w              s        2              ⁡          (              l        ,        m            )        =                    w                  s          1                    ⁡              (                  l          ,          m                )              ·          (                        α                      s            2                                    α                      s            1                              )        ·          e              j        ⁢                                  ⁢        2        ⁢                  π          ⁡                      (                                                            (                                                            k                      1                                        -                                          i                      1                                                        )                                ⁢                                  Δ                  1                                            +                                                (                                                            k                      2                                        -                                          i                      2                                                        )                                ⁢                                  Δ                  2                                                      )                              wheres1=i1N2+i2 and s2=k1N2+k2 (with 0≤i2<N2, 0≤i1<N1, 0≤k2<N2, and 0≤k1<N1) are integers identifying two entries of the beam w(l,m) so that (i1, i2) indicates to a first entry of beam w(l,m) that is mapped to a first antenna element (or port) and (k1, k2) indicates to a second entry of beam w(l,m) that is mapped to a second antenna element (or port).αs1=βi1γi2 and αs2=βk1γk2 are real numbers. αi≠1 (i=s1,s2) if magnitude tapering is used; otherwise αi=1.
      Δ    1    =      l                  O        1            ⁢              N        1            is a phase shift corresponding to a direction along an axis, e.g. the horizontal axis (“azimuth”).
      Δ    2    =      m                  O        2            ⁢              N        2            is a phase snip corresponding to direction along an axis, e.g. the vertical axis (“elevation”).
Therefore, a kth beam d(k) formed with precoder w(lk,mk) can also be referred to by the corresponding precoder w(lk,mk), i.e. d(k)=w(lk,mk). Thus a beam d(k) can be described as a set of complex numbers, each element of the set being characterized by at least one complex phase shift such that an element of the beam is related to any other element of the beam where dn(k)=di(k)αi,nej2π(pΔ1,k+qΔ2,k)=di(k)αi,n(ej2πΔ1,k)p(ej2πΔ2,k)q, where di(k) is the ith element of a beam d(k), αi,n is a real number corresponding to the ith and nth elements of the beam d(k); p and q are integers; and Δ1,k and Δ2,k are real numbers corresponding to a beam with index pair (lk,mk) that determine the complex phase shifts ej2πΔ1,k and ej2πΔ2,k, respectively. Index pair (lk,mk) corresponds to a direction of arrival or departure of a plane wave when beam d(k) is used for transmission or reception in a UPA or ULA. A beam d(k) can be identified with a single index k where =lk+N1O1mk, i.e, along vertical or N2 dimension first, or alternatively k=N2O2lk+mk, i.e. along horizontal or N1 dimension first.
Extending the precoder for a dual-polarized ULA may then be done as
                                          w                                          2                ⁢                D                            ,              DP                                ⁡                      (                          l              ,              m              ,              ϕ                        )                          =                                            [                                                                    1                                                                                                              e                                              j                        ⁢                                                                                                  ⁢                        ϕ                                                                                                        ]                        ⊗                                                            w                                      2                    ⁢                    D                                                  ⁡                                  (                                      l                    ,                    m                                    )                                            ⁡                              [                                                                                                                              w                                                      2                            ⁢                            D                                                                          ⁡                                                  (                                                      l                            ,                            m                                                    )                                                                                                                                                                                                  e                                                      j                            ⁢                                                                                                                  ⁢                            ϕ                                                                          ⁢                                                                              w                                                          2                              ⁢                              D                                                                                ⁡                                                      (                                                          l                              ,                              m                                                        )                                                                                                                                              ]                                              =                                                                 [                                                                                                                              w                                                      2                            ⁢                            D                                                                          ⁡                                                  (                                                      l                            ,                            m                                                    )                                                                                                            0                                                                                                  0                                                                                                                w                                                      2                            ⁢                            D                                                                          ⁡                                                  (                                                      l                            ,                            m                                                    )                                                                                                                    ]                            ⁡                              [                                                                            1                                                                                                                          e                                                  j                          ⁢                                                                                                          ⁢                          ϕ                                                                                                                    ]                                                                        Equation        ⁢                                  ⁢        3            
A precoder matrix W2D,DP for multi-layer transmission may be created by appending columns of DFT precoder vectors asW2D,DP(R)=[w2D,DP(l1,m1,ϕ1) w2D,DP(l2,m2,ϕ2) . . . w2D,DP(lR,mR,ϕR)]where R is the number of transmission layers, i.e. the transmission rank. In a special case for a rank-2 DFT precoder, m1=m2=m and l1=l2=l, there is
                                          W                                          2                ⁢                D                            ,              DP                                      (              2              )                                ⁡                      (                          l              ,              m              ,                              ϕ                1                            ,                              ϕ                2                                      )                          =                              [                                                                                                      w                                                                        2                          ⁢                          D                                                ,                        DP                                                              ⁡                                          (                                              l                        ,                        m                        ,                                                  ϕ                          1                                                                    )                                                                                                                                  w                                                                        2                          ⁢                          D                                                ,                        DP                                                              ⁡                                          (                                              l                        ,                        m                        ,                                                  ϕ                          2                                                                    )                                                                                            ]                    =                                                                 [                                                                                                                              w                                                      2                            ⁢                            D                                                                          ⁡                                                  (                                                      l                            ,                            m                                                    )                                                                                                            0                                                                                                  0                                                                                                                w                                                      2                            ⁢                            D                                                                          ⁡                                                  (                                                      l                            ,                            m                                                    )                                                                                                                    ]                            ⁡                              [                                                                            1                                                              1                                                                                                                          e                                                  j                          ⁢                                                                                                          ⁢                                                      ϕ                            1                                                                                                                                                              e                                                  j                          ⁢                                                                                                          ⁢                                                      ϕ                            2                                                                                                                                              ]                                                                        Eq        .                                  ⁢        1            For each rank, all the precoder candidates form a ‘precoder codebook’ or a ‘codebook’. A wireless device can first determine the rank of the estimated downlink wideband channel based on CSI-RS. After the rank is identified, for each subband the wireless device then searches through all the precoder candidates in a codebook for the determined rank to find the best precoder for the subband. For example, in case of rank=1, the wireless device would search through w2D,DP (k,l,ϕ) for all the possible (k,l,ϕ) values. In case of rank=2, the wireless device would search through W2D,DP(2)(k,l,ϕ1,ϕ2) for all the possible (k,l,ϕ1,ϕ2) values.MU-MIMO
With multi-user MIMO, two or more users in the same cell are co-scheduled on the same time-frequency resource. That is, two or more independent data streams are transmitted to different wireless devices at the same time, and the spatial domain is used to separate the respective streams. By transmitting several streams simultaneously, the capacity of the system can be increased. This however, comes at the cost of reducing the signal to interference plus noise ratio (SINR) per stream, as the power has to be shared between streams and the streams will cause interference to each-other.
When increasing the antenna array size, the increased beamforming gain will lead to higher SINR, however, as the user throughput depends only logarithmically on the SINR (for large SINRs), it is instead beneficial to trade the gains in SINR for a multiplexing gain, which increases linearly with the number of multiplexed wireless devices.
Accurate CSI is required in order to perform appropriate null-forming between co-scheduled users. In the current LTE 3GPP Release 13 (Rel.13) standard, no special CSI mode for multi-user (MU)-MIMO exists and thus, MU-MIMO scheduling and precoder construction has to be based on the existing CSI reporting designed for single-user MIMO (that is, a PMI indicating a DFT-based precoder, a RI and a CQI). This may prove quite challenging for MU-MIMO, as the reported precoder only contains information about the strongest channel direction for a user and may thus not contain enough information to do proper null-forming, which may lead to a large amount of interference between co-scheduled users, reducing the benefit of MU-MIMO.
Multi-Beam Precoders
The DFT-based precoders discussed above and used in LTE Rel-13 calculate cophasing across pairs of (typically differently polarized) ports. If more than one beam d(k) is used in CSI reporting, beams are not combined with the cophasing, but port pairs associated with a selected beam are cophased. Consequently, such DFT-based precoders can be considered as ‘single beam’ precoders. Multi-beam precoders are therefore an extension, where cophasing is applied across beams as well as port pairs. One such codebook is described herein. While the multi-beam codebook is described with two dimensions of the codebook relating to horizontal and vertical dimensions for concreteness, the codebook is equally applicable to a general case where the first or second dimension relates to horizontal or vertical antenna ports, as described above.
DN is defined as a size N×N DFT matrix, i.e. the elements of DN are defined as
            [              D        N            ]              k      ,      l        =            1              N              ⁢                  e                              j            ⁢                                                  ⁢            2            ⁢            π            ⁢                                                  ⁢            kl                    N                    .      Further, we define
            R      N        ⁡          (      q      )        =      diag    ⁡          (              [                                                            e                                  j                  ⁢                                                                          ⁢                  2                  ⁢                                      π                    ·                    0                    ·                                          q                      N                                                                                                                          e                                  j                  ⁢                                                                          ⁢                  2                  ⁢                                      π                    ·                    1                    ·                                          q                      N                                                                                                          …                                                      e                                  j                  ⁢                                                                          ⁢                  2                  ⁢                                      π                    ·                                          (                                              N                        -                        1                                            )                                        ·                                          q                      N                                                                                                          ]            )      to be a size N×N rotation matrix, defined for 0≤q<1. Multiplying DN with RN(q) from the left creates a rotated DFT matrix with entries
            [                                    R            N                    ⁡                      (            q            )                          ⁢                  D          N                    ]              k      ,      l        =            1              N              ⁢                  e                              j            ⁢                                                  ⁢            2            ⁢            π            ⁢                                                  ⁢                          k              ⁡                              (                                  l                  +                  q                                )                                              N                    .      The rotated DFT matrix RN(q)DN=[d1 d2 . . . dN] consist of normalized orthogonal column vectors {di}i=1N which furthermore span the vector space N. That is, the columns of RN(q)DN, for any q, is an orthonormal basis of N.
A codebook design extending the (rotated) DFT matrices that were appropriate transforms for a single-polarized uniform linear array (ULA) as discussed above to also fit the more general case of dual-polarized 2D uniform planar arrays (UPAs) is a starting point. A rotated 2D DFT matrix as DNV,NH(qV,qH)=(RNH(qH)DHH)⊗(RNV(qV)DNV)=[d1 d2 . . . dNVNH] is defined. The columns {di}i=1NDP of DNV,NH(qV,qH) constitutes an orthonormal basis of the vector space NVNH. Such a column di is henceforth denoted a (DFT) beam. A dual-polarized beam space transformation matrix suitable for a UPA is created, where the upper left and lower right elements correspond to the two polarizations:
            B                        N          V                ,                  N          H                      ⁡          (                        q          V                ,                  q          H                    )        =                    I        2            ⊗                        D                                    N              V                        ,                          N              H                                      ⁡                  (                                    q              V                        ,                          q              H                                )                      =                  [                                                                              D                                                            N                      V                                        ,                                          N                      H                                                                      ⁡                                  (                                                            q                      V                                        ,                                          q                      H                                                        )                                                                    0                                                          0                                                                        D                                                            N                      V                                        ,                                          N                      H                                                                      ⁡                                  (                                                            q                      V                                        ,                                          q                      H                                                        )                                                                    ]            =                                             [                                                                                d                    1                                                                                        d                    2                                                                    0                                                                      d                                                                  N                        V                                            ⁢                                              N                        H                                                                                                              0                                                  0                                                  …                                                  0                                                                              0                                                  0                                                  …                                                  0                                                                      d                    1                                                                                        d                    2                                                                    …                                                                      d                                                                  N                        V                                            ⁢                                              N                        H                                                                                                                  ]                    =                                                                 [                                                                                                    b                        1                                                                                                            b                        2                                                                                    …                                                                                      b                                                  2                          ⁢                                                      N                            V                                                    ⁢                                                      N                            H                                                                                                                                              ]                            ⁢                                                          .                                          The columns {bi}i=12NVNH of BNV,NH(qV,qH) constitute an orthonormal basis of the vector space 2NVNH. Such a column bi is henceforth denoted a single-polarized beam (SP-beam) as it is constructed by a beam d transmitted on a single polarization
      (                  i        .        e        .                                  ⁢        b            =                                    [                                                            d                                                                              0                                                      ]                    ⁢                                          ⁢          or          ⁢                                          ⁢          b                =                  [                                                    0                                                                    d                                              ]                      )    .The notation dual-polarized beam is introduced to refer to a beam transmitted on both polarizations (which are combined with a polarization cophasing factor ejα, i.e.
                    b        DP            =              [                                            d                                                                                            e                                      j                    ⁢                                                                                  ⁢                    α                                                  ⁢                d                                                    ]              )    .
Utilizing the assumption that the channel is somewhat sparse, sufficient channel energy is captured by only selecting a column subset of BNV,NH(qV,qH). That is, it is sufficient to describe a couple of the SP-beams, which keeps down the feedback overhead. So, select a column subset IS consisting of NSP columns of BNV,NH(qV,qH), to create a reduced beam space transformation matrix BIS=[bIS(1) bIS(2) . . . bIS(NSP)]. E.g., select column numbers IS=[1 5 10 25] to create the reduced beam space transformation matrix BIS=[b1 b5 b10 b25].
A general precoder structure for precoding of a single layer is:
  w  =                    B                  I          S                    ⁡              [                                                            c                1                                                                                        c                                  2                  ⁢                                                                                                                                                ⋮                                                                          c                                  N                  SP                                                                    ]              =                            [                                                                      b                                                            I                      S                                        ⁡                                          (                      1                      )                                                                                                                    b                                                            I                      S                                        ⁡                                          (                      2                      )                                                                                                  …                                                              b                                                            I                      S                                        ⁡                                          (                                              N                        SP                                            )                                                                                                    ]                ⁡                  [                                                                      c                  1                                                                                                      c                                      2                    ⁢                                                                                                                                                                    ⋮                                                                                      c                                      N                    SP                                                                                ]                    =                        ∑                      i            =            1                                N            SP                          ⁢                              c            i                    ⁢                                    b                                                I                  S                                ⁡                                  (                  i                  )                                                      .                              where {ci}i=1NSP are complex beam cophasing coefficients.The precoder w in the equation above is described as a linear combination of beams constructed by cophasing a kth beam bk with cophasing coefficient ck. Such a beam cophasing coefficient is a complex scalar that adjusts at least the phase of a beam relative to other beams according to ckbk. When a beam cophasing coefficient only adjusts relative phase, it is a unit magnitude complex number. It is in general desirable to also adjust the relative gain of beams, in which case the beam cophasing coefficient is not unit magnitude.
A more refined multi-beam precoder structure is achieved by separating the complex coefficients in a power (or amplitude) and a phase part as
  w  =                    B                  I          S                    ⁡              [                                                            c                1                                                                                        c                                  2                  ⁢                                                                                                                                                ⋮                                                                          c                                  N                  SP                                                                    ]              =                            B                      I            S                          ⁡                  [                                                                                                                p                      1                                                        ⁢                                      e                                          j                      ⁢                                                                                          ⁢                                              α                        1                                                                                                                                                                                                            p                      2                                                        ⁢                                      e                                          j                      ⁢                                                                                          ⁢                                              α                        2                                                                                                                                                ⋮                                                                                                                                p                                              N                        SP                                                                              ⁢                                      e                                          j                      ⁢                                                                                          ⁢                                              α                                                  N                          SP                                                                                                                                                  ]                    =                                                  B                              I                S                                      ⁡                          [                                                                                                                  p                        1                                                                                                                                                                                                    0                                                                                                                                                                                                                                                                                            0                                                                                                                                                                                                        p                        2                                                                                                                                                                                                    ⋱                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ⋱                                                        0                                                                                                                                                                                          ⋱                                                                                                                                                          0                                                                                                      p                                                  N                          SP                                                                                                                                ]                                ⁡                      [                                                                                e                                          j                      ⁢                                                                                          ⁢                                              α                        1                                                                                                                                                              e                                          j                      ⁢                                                                                          ⁢                                              α                        2                                                                                                                                          ⋮                                                                                                  e                                          j                      ⁢                                                                                          ⁢                                              α                                                  N                          SP                                                                                                                                          ]                          =                              B                          I              S                                ⁢                                    P                        ⁡                          [                                                                                          e                                              j                        ⁢                                                                                                  ⁢                                                  α                          1                                                                                                                                                                                e                                              j                        ⁢                                                                                                  ⁢                                                  α                          2                                                                                                                                                          ⋮                                                                                                              e                                              j                        ⁢                                                                                                  ⁢                                                  α                                                      N                            SP                                                                                                                                                          ]                                          As multiplying the precoder vector w with a complex constant C does not change its beamforming properties (as only the phase and amplitude relative to the other single-polarized beams is of importance), one may without loss of generality assume that the coefficients corresponding to e.g. SP-beam 1 is fixed to p1=1 and ejα1=1, so that parameters for one less beam needs to be signaled from the wireless device to the base station. Furthermore, the precoder may be further assumed to be multiplied with a normalization factor, so that e.g., a sum power constraint is fulfilled, i.e., that ∥w∥2=1. Any such normalization factor is omitted from the equations herein for clarity.
In some cases, the possible choices of columns of BNV,NH(qV,qH) are restricted so that if column i=i0 is chosen, so is column i=i0+NVNH. That is, if an SP-beam corresponding to a certain beam mapped to the first polarization is chosen, e.g.
            b              i        0              =          [                                                  d                              i                0                                                                          0                              ]        ,this would imply that the SP-beam
      b                  i        0            +                        N          V                ⁢                  N          H                      =      [                            0                                                  d                          i              0                                            ]  is chosen as well. That is, the SP-beam corresponding to the said certain beam mapped to the second polarization is chosen as well. This would reduce the feedback overhead as only NDP=NSP/2 columns of BNV,NH(qV,qH) would have to be selected and signaled back to the base station. In other words, the column selection is done on a beam (or DP-beam) level rather than an SP-beam level. If a certain beam is strong on one of the polarizations it would typically imply that the beam would be strong on the other polarization as well, at least in a wideband sense, so the loss of restricting the column selection in this way would not significantly decrease the performance. In the following discussion, the use of DP-beams is generally assumed (unless stated otherwise).
In some cases, the multi-beam precoder is factored into two or more factors that are selected with different frequency-granularity, in order to reduce the feedback overhead. In such cases, the SP-beam selection (i.e. the choice of matrix BIS) and the relative SP-beam powers/amplitudes (i.e. the choice of matrix √{square root over (P)}) is selected with a certain frequency-granularity while the SP-beam phases (i.e. the choice of matrix
         [                                        e                          j              ⁢                                                          ⁢                              α                1                                                                                      e                          j              ⁢                                                          ⁢                              α                2                                                                          ⋮                                                  e                          j              ⁢                                                          ⁢                              α                                  N                  SP                                                                          ]    )is selected with another certain frequency-granularity. In one such case, the said certain frequency-granularity corresponds to a wideband selection (that is, one selection for the entire bandwidth) while the said another certain frequency-granularity corresponds to a per-subband selection (that is, the carrier bandwidth is split into a number of subbands, typically consisting of 1-10 physical resource blocks (PRBs), and a separate selection is done for each subband).
In a typical such case, the multi-beam precoder vector is factored as w=W1W2, where W1 is selected with a certain frequency-granularity and W2 is selected with another certain frequency-granularity. The precoder vector may then be expressed as
  w  =                                          B                          I              S                                ⁢                      P                                    ︸                      =                          W              1                                          ⁢                        [                                                                      e                                      j                    ⁢                                                                                  ⁢                                          α                      1                                                                                                                                            e                                      j                    ⁢                                                                                  ⁢                                          α                      2                                                                                                                          ⋮                                                                                      e                                      j                    ⁢                                                                                  ⁢                                          α                                              N                        SP                                                                                                                          ]                          ︸                      =                          W              2                                            =                  W        1            ⁢                        W          2                .            Using this notation, if the said certain frequency-granularity corresponds to a wideband selection of W1 and the said another certain frequency-granularity corresponds to a per-subband selection of W2, the precoder vector for subband l may be expressed as wl=W1W2(l). That is, only W2 is a function of the subband index l.
Recently, 3GPP has specified a multi beam precoder design in its new advanced CSI codebook supporting one and two spatial layers with the following form in 3GPP TS 36.213 section 7.2.4, with 2 beams;
            W                        k          1                ,                  k          2                ,                              m                          1              ,                                ⁢                      m            2                          ,        p        ,                  q          1                ,                  q          2                ,                  q          3                    υ        =                  1                              P            ⁡                          (                              1                +                                  p                  2                                            )                                          ⁡              [                                                                              v                                                            k                      1                                        ,                                          k                      2                                                                      +                                  p                  ⁢                                                                          ⁢                                      φ                                          q                      3                                                        ⁢                                      v                                                                                            k                          1                                                +                                                  m                          1                                                                    ,                                                                        k                          2                                                +                                                  m                          2                                                                                                                                                                                                              φ                                      q                    1                                                  ⁡                                  (                                                            v                                                                        k                          1                                                ,                                                  k                          2                                                                                      +                                          p                      ⁢                                                                                          ⁢                                              φ                                                  q                          2                                                                    ⁢                                              v                                                                                                            k                              1                                                        +                                                          m                              1                                                                                ,                                                                                    k                              2                                                        +                                                          m                              2                                                                                                                                                            )                                                                    ]              ,          ⁢          ⁢      υ    =    1    ,  2For one layer:Wk1,k2m1,m2,p,q1,q2,q3(1)=Wk1,k2,m1,m2,p,q1,q2,q31,and for two layers:
      W                  k        1            ,              k        2            ,                        m                      1            ,                          ⁢                  m          2                    ,      p      ,              q                  1          ,          1                    ,              q                  2          ,          1                    ,              q                  3          ,          1                    ,              q                  1          ,          2                    ,                        q                      2            ,            2                          ⁢                  q                      3            ,            2                                      (      2      )        =            1              2              ⁡          [                                                  W                                                k                  1                                ,                                  k                  2                                ,                p                ,                                                      m                                          1                      ,                                                        ⁢                                      m                    2                                                  ,                                  q                                      1                    ,                    1                                                  ,                                  q                                      2                    ,                    1                                                  ,                                  q                                      3                    ,                    1                                                              1                                                          W                                                k                  1                                ,                                  k                  2                                ,                p                ,                                                      m                                          1                      ,                                                        ⁢                                      m                    2                                                  ,                                  q                                      1                    ,                    2                                                  ,                                  q                                      2                    ,                    2                                                  ,                                  q                                      3                    ,                    2                                                              2                                          ]      where:
            φ      n        =          e              j        ⁢                                  ⁢        π        ⁢                                  ⁢                  n          /          2                                u      m        =          [                                    1                                              e                              j                ⁢                                                      2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    m                                                                              O                      2                                        ⁢                                          N                      2                                                                                                                …                                              e                              j                ⁢                                                      2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                                          m                      ⁡                                              (                                                                              N                            2                                                    -                          1                                                )                                                                                                                        O                      2                                        ⁢                                          N                      2                                                                                                              ]                  v              l        ,        m              =                  [                                                            u                m                                                                                      e                                      j                    ⁢                                                                  2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                        l                                                                                              O                          1                                                ⁢                                                  N                          1                                                                                                                    ⁢                                  u                  m                                                                    …                                                                                                                  e                                              j                        ⁢                                                                              2                            ⁢                                                                                                                  ⁢                            π                            ⁢                                                                                                                  ⁢                                                          l                              ⁡                                                              (                                                                                                      N                                    1                                                                    -                                  1                                                                )                                                                                                                                                                        O                              1                                                        ⁢                                                          N                              1                                                                                                                                                                                                      u                      m                                                                                                          ]            T      Here, vl,m corresponds to a 2-dimensional beam bIS(i) as defined above. This is referred to as a 2 beam codebook in 3GPP, since vl,m and vk1+m1,k2+m2 are chosen on a wideband basis, and if an SP-beam vl,m or vk1+m1,k2+m2 corresponding to a certain beam mapped to the first polarization is chosen, e.g.
            b              i        0              =          [                                                  d                              i                0                                                                          0                              ]        ,this means that the SP-beam
      b                  i        0            +                        N          V                ⁢                  N          H                      =      [                            0                                                  d                          i              0                                            ]  is chosen, as described above. In this sense, there are two wideband dual polarized beams, and each of the 4 single polarized components of the 2 beams are combined independently on a subband basis. Therefore, the sums
         [                                                      v                                                k                  1                                ,                                  k                  2                                                      +                                          φ                                  q                  3                                            ⁢                              pv                                                                            k                      1                                        +                                          m                      1                                                        ,                                                            k                      2                                        +                                          m                      2                                                                                                                                                          φ                              q                1                                      ⁡                          (                                                v                                                            k                      1                                        ,                                          k                      2                                                                      +                                                                  ⁢                                                      φ                                          q                      2                                                        ⁢                                      pv                                                                                            k                          1                                                +                                                  m                          1                                                                    ,                                                                        k                          2                                                +                                                  m                          2                                                                                                                                )                                            ]  can be equivalently written as
            [                                                                                    c                  1                                ⁢                                  v                                                            k                      1                                        ,                                          k                      2                                                                                  +                                                c                  3                                ⁢                                  pv                                                                                    k                        1                                            +                                              m                        1                                                              ,                                                                  k                        2                                            +                                              m                        2                                                                                                                                                                                                      c                  2                                ⁢                                  v                                                            k                      1                                        ,                                          k                      2                                                                                  +                                                c                  4                                ⁢                                  pv                                                                                    k                        1                                            +                                              m                        1                                                              ,                                                                  k                        2                                            +                                              m                        2                                                                                                                                    ]        ⁡          [                                                                  ∑                                  i                  =                  0                                                                                            N                      SP                                        /                    2                                    -                  1                                            ⁢                                                c                                                            2                      ⁢                                                                                          ⁢                      i                                        +                    1                                                  ⁢                                  d                  i                                                                                                                        ∑                                  i                  =                  1                                                                      N                    SP                                    /                  2                                            ⁢                                                c                                      2                    ⁢                                                                                  ⁢                    i                                                  ⁢                                  d                  i                                                                        ]        =                    ∑                  i          =          1                          N          SP                    ⁢                        c          i                ⁢                  b                                    I              S                        ⁡                          (              i              )                                            =    w  with Nsp=2Ndp=4, with c1=1. It can also be observed from 3GPP TS 36.213 section 7.2.4 that indices q1, q2, and q3 correspond to the codebook index i2. The codebook index i2 can be a subband PMI, as it can be reported per subband, and corresponds to W2 as defined above. It can be observed that if p=0, that is if a single beam vk1,k2 is used, then only index q1 affects the value of Wk1,k2,m1,m2,p,q1,q2,q3ν, and so subband PMI for the first beam is identified by q1. Furthermore, q2, and q3 affect the relative phase of the second beam vk1+m1,k2+m2 to the first beam vk1,k2, and therefore can identify the subband PMI corresponding to a second beam.
Finally, the relative power p in 3GPP TS 36.213 is identified by a relative power indicator (‘RPI’), and designated as Ip therein.